Doklady Mathematics最新文献_第2页

Uniqueness and Explicit Solutions of a Mixed-Type Equation in the de Gennes Model de Gennes模型中混合型方程的唯一性和显式解

IF 0.8 4区数学

Doklady Mathematics Pub Date : 2026-07-05 DOI: 10.1134/S1064562426700067

M. D. Grubenko, A. M. Romanenkov, F. A. Tikhonov

{"title":"Uniqueness and Explicit Solutions of a Mixed-Type Equation in the de Gennes Model","authors":"M. D. Grubenko, A. M. Romanenkov, F. A. Tikhonov","doi":"10.1134/S1064562426700067","DOIUrl":"10.1134/S1064562426700067","url":null,"abstract":"This paper considers an initial boundary value problem for the linear wave equation in smectics in the de Gennes model, i.e., for a linear partial differential equation of mixed type with constant coefficients. For the original equation, we derive an integral identity that implies the energy conservation law, which is used to prove the uniqueness of a solution under homogeneous Dirichlet boundary conditions and zero initial conditions. For a rectangular parallelepiped domain with Dirichlet boundary conditions, an explicit solution is constructed using separation of variables. The solution is represented as a multidimensional Fourier series in terms of sine functions. The dispersion relation and formulas for the Fourier coefficients are written out in terms of initial data. The dimension (n = 4) is considered for the radially symmetric case in a cylindrical domain (with an annulus base). In this case, using the substitution (u = {v}{text{/}}r) simplifies the equation, the singularity at zero disappears, and the radial part of the solution is described by ordinary sines, rather than by Bessel functions. Explicit formulas for the eigenfrequencies and eigenfunctions are derived, and a series representation of the solution is obtained.","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 1","pages":"41 - 45"},"PeriodicalIF":0.8,"publicationDate":"2026-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Mathematical Model of Multistage Fourier Transform Based on Deductive Processing of Digital Signals 基于数字信号演绎处理的多级傅里叶变换数学模型

IF 0.8 4区数学

Doklady Mathematics Pub Date : 2026-07-05 DOI: 10.1134/S1064562426700043

A. S. Zinchenko, A. Yu. Burova

{"title":"Mathematical Model of Multistage Fourier Transform Based on Deductive Processing of Digital Signals","authors":"A. S. Zinchenko, A. Yu. Burova","doi":"10.1134/S1064562426700043","DOIUrl":"10.1134/S1064562426700043","url":null,"abstract":"Issues related to the mathematical modeling of the discrete Fourier transform of digital signals are considered. This study is motivated by the demand for research into additional optimization possibilities for digital signal processing algorithms. The purpose of the study is to reduce the computational complexity of the multistage Fourier transform. The study is based on difference digital filtering and the multistage Fourier transform. The results demonstrate and confirm the possibility of reducing the computational complexity of this transform based on deductive processing of digital signals. The concept of deductive signal processing is defined and described. We propose reducing the error of the multistage Fourier transform of digital signals by increasing their sampling frequency while decreasing the computational complexity of recurrent numerical algorithms for this transform by reducing the bit depth of difference samples of signals and difference samples of the impulse response of difference digital filtering. The practical significance of the research results consists in determining an additional reserve for improving the accuracy of the discrete Fourier transform of digital signals by applying their multistage Fourier transform based on deductive signal processing algorithms with an increase in the sampling frequency.","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 1","pages":"24 - 31"},"PeriodicalIF":0.8,"publicationDate":"2026-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Comparative Study of Optimization Models for Conceptual Aircraft Design under Uncertainty 不确定条件下概念飞机设计优化模型的比较研究

IF 0.8 4区数学

Doklady Mathematics Pub Date : 2026-07-05 DOI: 10.1134/S1064562426700055

G. S. Veresnikov, V. I. Goncharenko, D. N. Sobolev

{"title":"Comparative Study of Optimization Models for Conceptual Aircraft Design under Uncertainty","authors":"G. S. Veresnikov, V. I. Goncharenko, D. N. Sobolev","doi":"10.1134/S1064562426700055","DOIUrl":"10.1134/S1064562426700055","url":null,"abstract":"The development and comparative analysis of optimization models for the conceptual design of aircraft with nondeterministic input parameters are addressed using probability and uncertainty theories. Probability distribution functions describing the uncertainty of initial data are typically unknown at the stage of conceptual design. In this case, a possible approach to the construction of models with nondeterministic parameters is based on probability theory and frequency interpretations of uncertainties. To develop alternative optimization models designed to work with expert information, we chose uncertainty theory, which relies on principles similar to the generally accepted Kolmogorov axiomatics and allows for a reduction in computational costs by eliminating the requirement for measure additivity. The study focuses on the synthesis of reliable design solutions, which is of particular relevance in engineering practice. By formalizing the nondeterminism of the initial data using uncertain and random parameters, two sets of two-criteria models were developed that optimize the quantile and critical values of the objective functions. The objective functions are part of a computational algorithm that integrates aircraft parameter calculation models at the conceptual design stage. The results of a comparative analysis are presented, including computational costs and a comparison of Pareto fronts for different levels of uncertainty and reliability requirements.","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 1","pages":"32 - 40"},"PeriodicalIF":0.8,"publicationDate":"2026-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Modeling of Thermal Protection Based on Anisotropic Materials with a High Degree of Anisotropy 基于高度各向异性材料的热防护建模

IF 0.8 4区数学

Doklady Mathematics Pub Date : 2026-07-05 DOI: 10.1134/S1064562426700031

V. F. Formalev, B. A. Garibyan

{"title":"Modeling of Thermal Protection Based on Anisotropic Materials with a High Degree of Anisotropy","authors":"V. F. Formalev, B. A. Garibyan","doi":"10.1134/S1064562426700031","DOIUrl":"10.1134/S1064562426700031","url":null,"abstract":"This article describes a theoretically sound method for providing thermal protection for high-speed aircraft structural elements under aerogasdynamic heating conditions. The method involves posing and analytically solving the problem of heat transfer in a blunt nose section made of an anisotropic heat-shielding material with a high degree of anisotropy in one direction (the ratio of the maximum to the minimum component of the thermal conductivity tensor). A new analytical solution is obtained for this problem under conditions of heat exchange with the surrounding high-temperature medium (gasdynamic boundary layer) on the blunt body, in which the principal axis of the thermal conductivity tensor with the largest coefficient is directed along the body, and with the minimum coefficient, in the direction normal to the body surface. A situation arises in which the conductive heat flows from the forward stagnation point of the body and its vicinity, where the maximum heat fluxes are observed, to the tail section, thus significantly cooling the vicinity of the stagnation point. It becomes possible, at the thermal protection design stage, to control the characteristics of the thermal conductivity tensor (its principal components and the orientation of the principal axes relative to the selected coordinate system) to cool the most thermally loaded elements of the air vehicle structure. Numerical results have confirmed the effectiveness of this method of thermal protection for high-speed aircraft.","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 1","pages":"16 - 23"},"PeriodicalIF":0.8,"publicationDate":"2026-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Problems and Approaches to Storing and Analyzing Time Series under Conditions of Feature Redundancy 特征冗余条件下时间序列存储与分析的问题与方法

IF 0.8 4区数学

Doklady Mathematics Pub Date : 2026-05-05 DOI: 10.1134/S1064562426700018

O. V. Kozlova, S. S. Ilyukhina, E. A. Trunova

{"title":"Problems and Approaches to Storing and Analyzing Time Series under Conditions of Feature Redundancy","authors":"O. V. Kozlova, S. S. Ilyukhina, E. A. Trunova","doi":"10.1134/S1064562426700018","DOIUrl":"10.1134/S1064562426700018","url":null,"abstract":"The paper examines modern approaches to efficient storage and analysis of time series arising in monitoring industrial equipment, in particular, CNC machines. The main problem is the growth of data amount, which requires both the optimization of storage systems and the reduction of the dimension of input features without loss of information content. To solve the problem, we conducted a comparative analysis of purpose-built database management systems (DBMS): ClickHouse, InfluxDB, TimescaleDB, and PostgreSQL. Based on the testing results for ingestion rate, scalability, and resource consumption, ClickHouse was chosen. In parallel, we studied feature selection methods based on machine learning: L1 regularization, random forest, and gradient boosting. By using a real dataset of 18 material (wax) milling experiments, it was shown that gradient boosting (LightGBM) provides the best accuracy and robustness in feature importance evaluation. As a result, 20 most significant features related to position, speed, current, and voltage along the X, Y, and spindle S axes were identified. Based on these features, the condition of the tool, the completion of machining, and visual inspection results can be predicted with high reliability. The proposed approach allows one to reduce the amount of stored data, improve query performance, and reduce hardware costs for storing and processing time series.","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"113 1","pages":"1 - 8"},"PeriodicalIF":0.8,"publicationDate":"2026-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148380401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asymmetric Dynamic Resource Management Problem with Different Regimes 不同制度下的不对称动态资源管理问题

IF 0.6 4区数学

Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601003

V. V. Mazalov, A. N. Rettieva

引用次数: 0

An Example of Two Level Cooperation for Differential Game with Pairwise Interactions in Pollution Control Problems 污染控制问题中具有两两相互作用的微分对策的两层合作例子

IF 0.6 4区数学

Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601040

Y. He, L. A. Petrosyan

引用次数: 0

Adaptive Control for Two-Agent Opinion Dynamics under Uncertainty 不确定性下双主体意见动态的自适应控制

IF 0.6 4区数学

Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601143

Y. Chen, V. V. Mazalov, H. Gao

引用次数: 0

European Option Superhedging as an Antagonistic Game 欧洲期权超级对冲作为一种对抗性博弈

IF 0.6 4区数学

Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601015

O. V. Zverev, E. A. Shelemekh

{"title":"European Option Superhedging as an Antagonistic Game","authors":"O. V. Zverev, E. A. Shelemekh","doi":"10.1134/S1064562425601015","DOIUrl":"10.1134/S1064562425601015","url":null,"abstract":"In the article, the European option superhedging problem is identified with a dynamic stochastic zero-sum game between the market and the contract seller. The seller manages a portfolio of underlying assets in order to minimize her expected exponential risk. The market determines a probability distribution for discounted prices of traded assets: absolutely continuous with respect to a given underlying distribution and maximazing seller’s expected risk. Recurrence relations for the upper and lower values of the game are obtained. It is shown that the absence of arbitrage opportunities in the market is a necessary and sufficient condition for the existence of a self-financing portfolio, with which the lower bound in the definition of the upper value of the game is obtained. Such a portfolio is superhedging, and the upper value of the game allows one to calculate the upper hedging price. Moreover, it is shown that, in a market model without arbitrage opportunities, there is always a game equilibrium. The saddle point of the game, if it exists, determines a superhedging portfolio and a martingale probability distribution, with which an upper bound in the definition of the upper value of the game is achieved. This distribution defines the seller’s worst market in the sense that the reserve of the superhedging portfolio is fully consumed in that market model. Using examples, we provide comparison between results of option calculations based on probabilistic and trajectory-based game approaches, analyze advantages and disadvantages of the topology choice ((sigma ({{L}^{1}},{{L}^{infty }})) topology instead of weak topology) in the probabilistic formulation of this type of problems.","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"112 1","pages":"S86 - S102"},"PeriodicalIF":0.6,"publicationDate":"2026-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147686632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bi-Criterial Approach to Optimization Problems with Uncertain Factors 不确定因素优化问题的双准则方法

IF 0.6 4区数学

Doklady Mathematics Pub Date : 2026-04-16 DOI: 10.1134/S1064562425601027

I. V. Konnov

引用次数: 0